1. **State the problem:** We have a cuboid carton with base dimensions 14 cm by 12 cm and height 18 cm. It is filled with water to a depth of 12 cm. When the carton is turned over so the shaded side (originally a side face) is facing upwards, we need to find the new water depth $d$. 2. **Calculate the volume of water initially:** The volume of water is the base area times the water height: $$V = 14 \times 12 \times 12 = 2016 \text{ cm}^3$$ 3. **Identify the new base dimensions when turned over:** The shaded side facing upwards means the base is now 14 cm by 18 cm (the original height becomes the base depth). 4. **Use the volume to find the new water depth $d$:** Since volume remains constant, $$V = \text{new base area} \times d = 14 \times 18 \times d$$ 5. **Solve for $d$:** $$d = \frac{V}{14 \times 18} = \frac{2016}{252} = 8 \text{ cm}$$ **Final answer:** $$d = 8 \text{ cm}$$